Relationship To Provability
The result that MU cannot be obtained with these rules demonstrates the notion of independence in mathematical logic. The MIU system can be viewed as a formal logic in which a string is considered provable if it can be derived by application of the rules starting from MI. In this interpretation, the question is phrased as "Is MU provable in the MIU logic?".
Finding an invariant of the inference rules is a common method for establishing independence results.
Read more about this topic: MU Puzzle
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